TSTP Solution File: LCL833-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL833-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:58:35 EDT 2022
% Result : Timeout 300.10s 300.61s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : LCL833-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 3 04:59:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.88/1.24 *** allocated 10000 integers for termspace/termends
% 0.88/1.24 *** allocated 10000 integers for clauses
% 0.88/1.24 *** allocated 10000 integers for justifications
% 0.88/1.24 *** allocated 15000 integers for termspace/termends
% 0.88/1.24 Bliksem 1.12
% 0.88/1.24
% 0.88/1.24
% 0.88/1.24 Automatic Strategy Selection
% 0.88/1.24
% 0.88/1.24 Clauses:
% 0.88/1.24 [
% 0.88/1.24 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.88/1.24 ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.88/1.24 ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.24 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.24 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.24 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.24 ,
% 0.88/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.24 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.88/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 0.88/1.24 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.24 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 0.88/1.24 ,
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.24 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.88/1.24 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.88/1.24 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ),
% 0.88/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.88/1.24 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.24 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.88/1.24 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.24 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ],
% 0.88/1.24 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.24 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.88/1.24 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.24 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.88/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.24 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.24 , Y, X ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.88/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.88/1.24 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.88/1.24 ) ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.24 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.88/1.24 ) ) ],
% 0.88/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.88/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ) ), =( Y, Z ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.88/1.24 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.24 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.88/1.24 'tc_nat' ) ) ],
% 0.88/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.24 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.88/1.24 'tc_nat' ) ) ],
% 0.88/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.24 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.24 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.88/1.24 , X ) ), T, X ) ) ],
% 0.88/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.24 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.24 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.88/1.24 ), Z ), T, X ) ) ],
% 0.88/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.88/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.88/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.88/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.88/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP( hAPP(
% 0.88/1.24 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.88/1.24 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.24 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.88/1.24 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.24 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.88/1.24 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.24 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.88/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.24 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 'tc_nat' ), Z ), T ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.24 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.24 Y, T, X ), X ) ) ],
% 0.88/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.24 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.24 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.88/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.88/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.88/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 X ), Y ), Z ) ), T ) ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.88/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.24 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.88/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.88/1.24 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.88/1.24 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.88/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), Y ), Z ) ), T ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.25 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.25 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 0.88/1.25 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.88/1.25 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.88/1.25 ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.88/1.25 ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.88/1.25 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Z, T, 'tc_nat' ), X ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.88/1.25 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 Z, X, 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, Z, X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, Z, X ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.88/1.25 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.88/1.25 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.25 , Y, X ), X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.25 , Z, X ), X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.25 , Z, X ), X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.88/1.25 , X, 'tc_nat' ), X ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.88/1.25 ), 'tc_nat' ), X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.88/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), 'c_Divides_Odiv__class_Odiv'(
% 0.88/1.25 Z, T, X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y
% 0.88/1.25 , X ), X ) ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ), T ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 0.88/1.25 ), Z, X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.25 , T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.25 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.25 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.25 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.88/1.25 ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.88/1.25 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ) ) ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 X, T, 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.88/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.88/1.25 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.88/1.25 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.88/1.25 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.88/1.25 , Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.88/1.25 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.88/1.25 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.88/1.25 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.88/1.25 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.25 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.88/1.25 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.25 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.25 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.88/1.25 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.88/1.25 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.88/1.25 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.88/1.25 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.88/1.25 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.88/1.25 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.88/1.25 , T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.88/1.25 ) ), 'c_Suc'( Z ) ), hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.88/1.25 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.88/1.25 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.88/1.25 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.25 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.25 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 0.88/1.25 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat'
% 0.88/1.25 ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.88/1.25 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 0.88/1.25 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 Y, 'tc_nat' ) ), Z ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), T ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 0.88/1.25 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.88/1.25 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.25 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.25 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.25 , 'tc_nat' ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.88/1.25 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.88/1.25 , 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.88/1.25 , 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.88/1.25 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.88/1.25 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 , X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.88/1.25 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.88/1.25 , Z ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.88/1.25 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.88/1.25 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.25 , T, X ), X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.88/1.25 Y, Z, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Z ), T ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.88/1.25 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.88/1.25 , X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X
% 0.88/1.25 ) ), 'c_HOL_Oone__class_Oone'( X ) ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.88/1.25 X ), Y ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.88/1.25 X ), Y ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.25 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.88/1.25 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.88/1.25 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.25 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.88/1.25 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.88/1.25 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.88/1.25 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 Y, 'tc_nat' ) ), Z ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.88/1.25 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.88/1.25 =( Y, T ), =( X, Z ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.88/1.25 =( Y, T ), =( X, Z ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.88/1.25 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.88/1.25 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.25 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.88/1.25 X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.25 ), Z ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), Z
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, Y
% 0.88/1.25 , X ) ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.88/1.25 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.88/1.25 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 0.88/1.25 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ) ) ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.25 ), =( Z, Y ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.25 ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.88/1.25 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.88/1.25 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.25 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.25 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 T, X ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.88/1.25 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), Z, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'(
% 0.88/1.25 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.88/1.25 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.88/1.25 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.88/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.88/1.25 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.88/1.25 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.25 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.25 , Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.25 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.88/1.25 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.25 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.88/1.25 Y ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.88/1.25 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.25 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.88/1.25 , Y ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.88/1.25 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 0.88/1.25 hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~(
% 0.88/1.25 hBOOL( hAPP( X, Y ) ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.88/1.25 X ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 0.88/1.25 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 0.88/1.25 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.88/1.25 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.88/1.25 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 0.88/1.25 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.88/1.25 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.88/1.25 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.88/1.25 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinducts__1'(
% 0.88/1.25 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.88/1.25 ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinduct__1'(
% 0.88/1.25 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ), 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ), 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xupt__Xinduct__1'(
% 0.88/1.25 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.88/1.25 ],
% 0.88/1.25 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ) ), X, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.25 ) ), X, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.88/1.25 ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.88/1.25 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.88/1.25 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.88/1.25 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 Y ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.88/1.25 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.88/1.25 ) ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.88/1.25 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.88/1.25 Y ) ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.88/1.25 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.88/1.25 Z ) ) ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.88/1.25 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.88/1.25 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.88/1.25 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.88/1.25 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.88/1.25 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.88/1.25 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.88/1.25 Z ) ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.88/1.25 , X ), 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.88/1.25 ), Z ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.88/1.25 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.88/1.25 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.88/1.25 , 'c_List_Olist_ONil'( T ) ) ],
% 0.88/1.25 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.88/1.25 'c_List_Olist_ONil'( Z ) ) ],
% 0.88/1.25 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.88/1.25 ), Z, X ) ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), X ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.88/1.25 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.88/1.25 ), X ), Y ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ),
% 0.88/1.25 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~( 'c_Lambda_Obeta'(
% 0.88/1.25 X, T ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 0.88/1.25 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 0.88/1.25 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.88/1.25 U ), Z ) ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X ) ), Y ),
% 0.88/1.25 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ) ) ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.88/1.25 , 'v_a____' ), X ), Y ) ) ), ~( 'c_Type_Otyping'( Z, X, 'v_T____' ) ),
% 0.88/1.25 ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ), ~( 'c_Type_Otyping'(
% 0.88/1.25 'c_Type_Oshift'( Z, Y, 'v_T____', 'tc_Type_Otype' ), 'v_a____', T ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.88/1.25 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.88/1.25 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, U, 'tc_nat' ) ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' )
% 0.88/1.25 , 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.88/1.25 X ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.25 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.88/1.25 ), Y, X ) ), =( Z, T ) ],
% 0.88/1.25 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.25 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.88/1.25 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.88/1.25 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.88/1.25 , X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.88/1.25 , X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.25 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.25 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 0.88/1.25 ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.88/1.25 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.25 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.25 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.88/1.25 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.25 , Y, X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'(
% 0.88/1.25 Y, Z, 'tc_nat' ), 'tc_nat' ) ), T ), 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) )
% 0.88/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 0.88/1.25 , 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.25 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, U
% 0.88/1.25 , X ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.88/1.25 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.88/1.25 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 0.88/1.25 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.88/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.88/1.25 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.88/1.25 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.88/1.25 ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.88/1.25 , Z ), Y ), 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.88/1.25 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.88/1.25 ],
% 0.88/1.25 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 0.88/1.25 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.88/1.25 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 0.88/1.25 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.88/1.25 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.88/1.25 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.88/1.25 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.88/1.25 ) ],
% 0.88/1.25 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 0.88/1.25 ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X )
% 0.88/1.25 , Z, X ) ), Y ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.25 ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.25 , Y, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.25 , T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.25 , T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.25 , Y, X ), X ) ) ],
% 0.88/1.25 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.25 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.88/1.25 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.88/1.25 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), T ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.88/1.25 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.88/1.25 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 0.88/1.25 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ) ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.25 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.88/1.25 , X ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.25 T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.25 X ), Z, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.25 T, X ), X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.25 X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.25 T, X ), X ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.25 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.25 X ), T, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Z, T, X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.88/1.25 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Z, T, X ) ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.88/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.25 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.25 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.25 Y, T, X ) ) ) ],
% 0.88/1.25 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 0.88/1.25 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.25 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.25 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.25 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.25 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.88/1.25 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.88/1.25 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.88/1.25 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.25 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.88/1.25 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.88/1.25 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.88/1.25 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.25 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1'( X ) )
% 0.88/1.25 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL(
% 0.88/1.25 hAPP( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) )
% 0.88/1.25 ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.88/1.25 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.25 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.88/1.25 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.88/1.25 'c_Suc'( Y ), Z, T ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 0.88/1.25 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1'( X ) )
% 0.88/1.25 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.88/1.25 ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.88/1.25 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.88/1.25 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.88/1.25 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1'( X
% 0.88/1.25 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 0.88/1.25 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.25 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.25 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.88/1.25 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.88/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.25 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 0.88/1.25 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.88/1.25 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.88/1.25 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.88/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.88/1.25 ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.88/1.25 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.88/1.25 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.88/1.25 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 0.88/1.25 ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.88/1.25 , Y ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.88/1.25 , 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.88/1.25 ) ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OAbs'( X ) ), Y
% 0.88/1.25 ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.88/1.25 hAPP( hAPP( 'c_Lambda_Olift', Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.25 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.88/1.25 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 0.88/1.25 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.88/1.25 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.88/1.25 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.88/1.25 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.88/1.25 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.88/1.25 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 0.88/1.25 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.88/1.25 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ),
% 0.88/1.25 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'v_T_H____' ) ],
% 0.88/1.25 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', 'c_Lambda_Oliftn'( X, Y, Z ) ), Z ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.88/1.25 , X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL( hAPP(
% 0.88/1.25 'c_InductTermi_OIT', X ) ) ) ],
% 0.88/1.25 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.88/1.25 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 0.88/1.25 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.88/1.25 'c_Type_Otypings'( X, T, U ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.88/1.25 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.88/1.25 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ) ],
% 0.88/1.25 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.88/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.88/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.88/1.25 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.88/1.25 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.88/1.25 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Osubst', 'v_r____' ), 'v_a____' ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.25 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ), Y )
% 0.88/1.25 ) ), ~( 'c_Type_Otyping'( Z, X, 'v_T____' ) ), ~( hBOOL( hAPP(
% 0.88/1.25 'c_InductTermi_OIT', X ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( Z, Y
% 0.88/1.25 , 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_r____' ), 'v_a____' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), T ) ) ],
% 0.88/1.25 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.88/1.25 X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.88/1.25 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.88/1.25 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.88/1.25 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 0.88/1.25 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_a____' ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.88/1.25 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.88/1.25 Z ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.88/1.25 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_r____' ), 'v_a____' ),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.88/1.25 Z ) ) ) ],
% 0.88/1.25 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.88/1.25 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 0.88/1.25 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 0.88/1.25 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.88/1.25 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.88/1.25 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.88/1.25 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.88/1.25 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.88/1.25 ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.88/1.25 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.88/1.25 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.88/1.25 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.88/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.88/1.25 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.88/1.25 , 'tc_Lambda_OdB' ) ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.25 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.25 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.88/1.25 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 0.88/1.25 ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.88/1.25 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.88/1.25 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.88/1.25 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.88/1.25 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.88/1.25 , 'tc_Lambda_OdB' ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.25 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.25 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.88/1.25 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.88/1.25 , Y ) ],
% 0.88/1.25 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.88/1.25 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.88/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.88/1.25 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.88/1.25 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ],
% 0.88/1.25 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 0.88/1.25 X ), Y ) ), Z ), Y ), X ) ],
% 0.88/1.25 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.88/1.25 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.88/1.25 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_r____' ), hAPP( hAPP(
% 0.88/1.25 'c_Lambda_Olift', 'v_u____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 0.88/1.25 , 'c_Suc'( 'v_i____' ) ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.88/1.25 'v_a____' ), 'v_u____' ), 'v_i____' ) ), 'c_List_Omap'( 'c_COMBC'(
% 0.88/1.25 'c_COMBC'( 'c_Lambda_Osubst', 'v_u____', 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.88/1.25 , 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_i____', 'tc_Lambda_OdB',
% 0.88/1.25 'tc_nat', 'tc_Lambda_OdB' ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.88/1.25 ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.88/1.25 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.88/1.25 'class_Orderings_Opreorder'( Y ) ) ],
% 0.88/1.25 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.88/1.25 'class_Orderings_Oorder'( Y ) ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.88/1.25 ],
% 0.88/1.25 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.88/1.25 ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.88/1.25 ],
% 0.88/1.25 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.88/1.25 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.88/1.25 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.88/1.25 ,
% 0.88/1.25 [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) ) ) ],
% 0.88/1.25 [ 'c_fequal'( X, X, Y ) ],
% 0.88/1.25 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.88/1.25 ] .
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 percentage equality = 0.347082, percentage horn = 0.869338
% 0.88/1.25 This is a problem with some equality
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25
% 0.88/1.25 Options Used:
% 0.88/1.25
% 0.88/1.25 useres = 1
% 0.88/1.25 useparamod = 1
% 0.88/1.25 useeqrefl = 1
% 0.88/1.25 useeqfact = 1
% 0.88/1.25 usefactor = 1
% 0.88/1.25 usesimpsplitting = 0
% 0.88/1.25 usesimpdemod = 5
% 0.88/1.25 usesimpres = 3
% 0.88/1.25
% 0.88/1.25 resimpinuse = 1000
% 0.88/1.25 resimpclauses = 20000
% 0.88/1.25 substype = eqrewr
% 0.88/1.25 backwardsubs = 1
% 0.88/1.25 selectoldest = 5
% 0.88/1.25
% 0.88/1.25 litorderings [0] = split
% 0.88/1.25 litorderings [1] = extend the termordering, first sorting on arguments
% 0.88/1.25
% 0.88/1.25 termordering = kbo
% 0.88/1.25
% 0.88/1.25 litapriori = 0
% 0.88/1.25 termapriori = 1
% 0.88/1.25 litaposteriori = 0
% 0.88/1.25 termaposteriori = 0
% 0.88/1.25 demodaposteriori = 0
% 0.88/1.25 ordereqreflfact = 0
% 0.88/1.25
% 0.88/1.25 litselect = negord
% 0.88/1.25
% 0.88/1.25 maxweight = 15
% 0.88/1.25 maxdepth = 30000
% 0.88/1.25 maxlength = 115
% 0.88/1.25 maxnrvars = 195
% 0.88/1.25 excuselevel = 1
% 0.88/1.25 increasemaxweight = 1
% 0.88/1.25
% 0.88/1.25 maxselected = 10000000
% 0.88/1.25 maxnrclauses = 10000000
% 0.88/1.25
% 0.88/1.25 showgenerated = 0
% 0.88/1.25 showkept = 0
% 0.88/1.25 showselected = 0
% 0.88/1.25 showdeleted = 0
% 0.88/1.25 showresimp = 1
% 0.88/1.25 showstatus = 2000
% 0.88/1.25
% 0.88/1.25 prologoutput = 1
% 0.88/1.25 nrgoals = 5000000
% 0.88/1.25 totalproof = 1
% 0.88/1.25
% 0.88/1.25 Symbols occurring in the translation:
% 0.88/1.25
% 0.88/1.25 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.25 . [1, 2] (w:1, o:149, a:1, s:1, b:0),
% 0.88/1.25 ! [4, 1] (w:0, o:87, a:1, s:1, b:0),
% 0.88/1.25 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.25 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.25 'c_Lambda_OdB_OVar' [41, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.88/1.25 hAPP [42, 2] (w:1, o:174, a:1, s:1, b:0),
% 0.88/1.25 'c_Type_Otyping' [43, 3] (w:1, o:178, a:1, s:1, b:0),
% 0.88/1.25 'tc_nat' [44, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.88/1.25 'c_HOL_Ozero__class_Ozero' [45, 1] (w:1, o:93, a:1, s:1, b:0),
% 0.88/1.25 'c_HOL_Oord__class_Oless' [47, 3] (w:1, o:179, a:1, s:1, b:0),
% 0.88/1.25 'c_HOL_Otimes__class_Otimes' [49, 3] (w:1, o:180, a:1, s:1, b:0),
% 0.88/1.25 'class_OrderedGroup_Opordered__comm__monoid__add' [51, 1] (w:1, o:95
% 0.88/1.25 , a:1, s:1, b:0),
% 0.88/1.25 'c_HOL_Oplus__class_Oplus' [52, 1] (w:1, o:97, a:1, s:1, b:0),
% 0.88/1.25 'class_Divides_Osemiring__div' [55, 1] (w:1, o:98, a:1, s:1, b:0),
% 0.88/1.25 'c_Divides_Odiv__class_Omod' [56, 3] (w:1, o:181, a:1, s:1, b:0),
% 0.88/1.25 'c_Ring__and__Field_Odvd__class_Odvd' [57, 3] (w:1, o:182, a:1, s:1
% 0.88/1.25 , b:0),
% 0.88/1.25 'c_Divides_Odiv__class_Odiv' [58, 3] (w:1, o:183, a:1, s:1, b:0),
% 0.88/1.25 'class_Ring__and__Field_Oordered__ring__strict' [60, 1] (w:1, o:101
% 0.88/1.25 , a:1, s:1, b:0),
% 0.88/1.25 'c_Lambda_Olift' [61, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.88/1.25 'c_Lambda_Osubst' [62, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.88/1.25 'c_HOL_Oone__class_Oone' [67, 1] (w:1, o:96, a:1, s:1, b:0),
% 0.88/1.25 'class_Ring__and__Field_Osemiring' [68, 1] (w:1, o:104, a:1, s:1, b:0
% 0.88/1.25 ),
% 0.88/1.25 'class_Ring__and__Field_Oordered__semidom' [72, 1] (w:1, o:105, a:1
% 0.88/1.25 , s:1, b:0),
% 0.88/1.25 'c_Power_Opower__class_Opower' [73, 3] (w:1, o:184, a:1, s:1, b:0),
% 0.88/1.25 'class_Ring__and__Field_Osemiring__1' [74, 1] (w:1, o:107, a:1, s:1
% 0.88/1.25 , b:0),
% 0.88/1.25 'c_Suc' [75, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.88/1.25 'c_Nat_Osemiring__1__class_Oof__nat' [76, 2] (w:1, o:175, a:1, s:1
% 0.88/1.25 , b:0),
% 0.88/1.25 'class_OrderedGroup_Omonoid__mult' [79, 1] (w:1, o:110, a:1, s:1, b:0
% 0.88/1.25 ),
% 0.88/1.25 'class_OrderedGroup_Oab__group__add' [80, 1] (w:1, o:111, a:1, s:1
% 0.88/1.25 , b:0),
% 0.88/1.25 'class_Ring__and__Field_Ocomm__semiring__1' [81, 1] (w:1, o:112, a:1
% 0.88/1.25 , s:1, b:0),
% 0.88/1.25 'class_OrderedGroup_Oab__semigroup__add' [83, 1] (w:1, o:113, a:1, s:
% 0.88/1.25 1, b:0),
% 0.88/1.25 'class_OrderedGroup_Ocomm__monoid__add' [84, 1] (w:1, o:114, a:1, s:1
% 0.88/1.25 , b:0),
% 0.88/1.25 'class_Orderings_Oorder' [85, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.88/1.25 'class_Orderings_Opreorder' [86, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.88/1.25 'class_Power_Opower' [88, 1] (w:1, o:127, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Oidom' [90, 1] (w:1, o:128, a:1, s:1, b:0),
% 9.45/9.87 'class_Int_Onumber__ring' [91, 1] (w:1, o:129, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Odvd' [92, 1] (w:1, o:131, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Ocomm__monoid__mult' [93, 1] (w:1, o:117, a:1, s:
% 9.45/9.87 1, b:0),
% 9.45/9.87 'c_List_Olist_ONil' [95, 1] (w:1, o:132, a:1, s:1, b:0),
% 9.45/9.87 'c_List_Olistsp' [96, 3] (w:1, o:185, a:1, s:1, b:0),
% 9.45/9.87 'c_Lambda_OdB_OAbs' [98, 1] (w:1, o:133, a:1, s:1, b:0),
% 9.45/9.87 'c_Lambda_Osubstn' [99, 3] (w:1, o:186, a:1, s:1, b:0),
% 9.45/9.87 'class_Nat_Osemiring__char__0' [101, 1] (w:1, o:94, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Ocancel__ab__semigroup__add' [102, 1] (w:1, o:118
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Ocancel__semigroup__add' [103, 1] (w:1, o:119, a:
% 9.45/9.87 1, s:1, b:0),
% 9.45/9.87 'c_Lambda_Oliftn' [104, 3] (w:1, o:187, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Oordered__semiring__strict' [105, 1] (w:1, o:
% 9.45/9.87 134, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Oordered__comm__semiring__strict' [106, 1]
% 9.45/9.87 (w:1, o:135, a:1, s:1, b:0),
% 9.45/9.87 'tc_Type_Otype' [109, 0] (w:1, o:62, a:1, s:1, b:0),
% 9.45/9.87 'c_Type_Oshift' [110, 4] (w:1, o:190, a:1, s:1, b:0),
% 9.45/9.87 hBOOL [113, 1] (w:1, o:136, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Olordered__ab__group__add' [114, 1] (w:1, o:109
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Ozero__neq__one' [115, 1] (w:1, o:137, a:1
% 9.45/9.87 , s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Ono__zero__divisors' [116, 1] (w:1, o:100, a:
% 9.45/9.87 1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Omult__zero' [117, 1] (w:1, o:99, a:1, s:1
% 9.45/9.87 , b:0),
% 9.45/9.87 'class_Ring__and__Field_Oring__1__no__zero__divisors' [118, 1] (w:1
% 9.45/9.87 , o:102, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Oring__no__zero__divisors' [119, 1] (w:1, o:
% 9.45/9.87 103, a:1, s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Oordered__idom' [122, 1] (w:1, o:138, a:1, s:
% 9.45/9.87 1, b:0),
% 9.45/9.87 'class_Orderings_Olinorder' [128, 1] (w:1, o:120, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [129, 1]
% 9.45/9.87 (w:1, o:121, a:1, s:1, b:0),
% 9.45/9.87 'c_Lambda_Obeta' [130, 2] (w:1, o:176, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Oab__semigroup__idem__mult' [131, 1] (w:1, o:122
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Omonoid__add' [132, 1] (w:1, o:123, a:1, s:1, b:0
% 9.45/9.87 ),
% 9.45/9.87 'class_Ring__and__Field_Osemiring__0' [133, 1] (w:1, o:106, a:1, s:1
% 9.45/9.87 , b:0),
% 9.45/9.87 'v_sko__List__Xlexn__Xinduct__1' [135, 1] (w:1, o:139, a:1, s:1, b:0)
% 9.45/9.87 ,
% 9.45/9.87 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1' [136, 1] (w:1, o:140
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1' [137, 1] (w:1, o:141
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'v_sko__List__Xreplicate__Xinduct__1' [138, 1] (w:1, o:142, a:1, s:1
% 9.45/9.87 , b:0),
% 9.45/9.87 'v_sko__Nat__Xnat__Xinducts__1' [139, 1] (w:1, o:143, a:1, s:1, b:0)
% 9.45/9.87 ,
% 9.45/9.87 'v_sko__Nat__Xnat__Xinduct__1' [140, 1] (w:1, o:144, a:1, s:1, b:0),
% 9.45/9.87
% 9.45/9.87 'v_sko__List__Xupt__Xinduct__1' [141, 1] (w:1, o:145, a:1, s:1, b:0)
% 9.45/9.87 ,
% 9.45/9.87 'c_Lambda_OdB_OApp' [142, 0] (w:1, o:65, a:1, s:1, b:0),
% 9.45/9.87 'c_List_Omap' [149, 4] (w:1, o:191, a:1, s:1, b:0),
% 9.45/9.87 'tc_Lambda_OdB' [151, 0] (w:1, o:68, a:1, s:1, b:0),
% 9.45/9.87 'c_List_Ofoldl' [152, 5] (w:1, o:192, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Osemigroup__add' [154, 1] (w:1, o:124, a:1, s:1
% 9.45/9.87 , b:0),
% 9.45/9.87 'c_InductTermi_OIT' [158, 0] (w:1, o:70, a:1, s:1, b:0),
% 9.45/9.87 'v_a____' [159, 0] (w:1, o:71, a:1, s:1, b:0),
% 9.45/9.87 'v_T____' [160, 0] (w:1, o:72, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [165, 1]
% 9.45/9.87 (w:1, o:125, a:1, s:1, b:0),
% 9.45/9.87 'v_e____' [168, 0] (w:1, o:74, a:1, s:1, b:0),
% 9.45/9.87 'v_u____' [169, 0] (w:1, o:75, a:1, s:1, b:0),
% 9.45/9.87 'class_OrderedGroup_Oab__semigroup__mult' [170, 1] (w:1, o:126, a:1
% 9.45/9.87 , s:1, b:0),
% 9.45/9.87 'class_Ring__and__Field_Ocomm__semiring' [171, 1] (w:1, o:130, a:1
% 9.45/9.87 , s:1, b:0),
% 9.45/9.87 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1' [172, 1] (w:1, o:146
% 9.45/9.87 , a:1, s:1, b:0),
% 9.45/9.87 'c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1' [173, 1] (w:1, o:147
% 38.11/38.52 , a:1, s:1, b:0),
% 38.11/38.52 'c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1' [174, 1] (w:1
% 38.11/38.52 , o:148, a:1, s:1, b:0),
% 38.11/38.52 'tc_fun' [175, 2] (w:1, o:177, a:1, s:1, b:0),
% 38.11/38.52 'c_COMBC' [176, 5] (w:1, o:193, a:1, s:1, b:0),
% 38.11/38.52 'c_Type_Otypings' [178, 3] (w:1, o:188, a:1, s:1, b:0),
% 38.11/38.52 'v_i____' [179, 0] (w:1, o:76, a:1, s:1, b:0),
% 38.11/38.52 'v_r____' [180, 0] (w:1, o:77, a:1, s:1, b:0),
% 38.11/38.52 'v_as____' [181, 0] (w:1, o:78, a:1, s:1, b:0),
% 38.11/38.52 'v_T_H____' [182, 0] (w:1, o:79, a:1, s:1, b:0),
% 38.11/38.52 'c_COMBB' [191, 6] (w:1, o:194, a:1, s:1, b:0),
% 38.11/38.52 'c_fequal' [192, 3] (w:1, o:189, a:1, s:1, b:0).
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Starting Search:
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 4442
% 38.11/38.52 Kept: 2002
% 38.11/38.52 Inuse: 139
% 38.11/38.52 Deleted: 6
% 38.11/38.52 Deletedinuse: 0
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 13051
% 38.11/38.52 Kept: 4218
% 38.11/38.52 Inuse: 276
% 38.11/38.52 Deleted: 10
% 38.11/38.52 Deletedinuse: 0
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 21394
% 38.11/38.52 Kept: 6240
% 38.11/38.52 Inuse: 373
% 38.11/38.52 Deleted: 13
% 38.11/38.52 Deletedinuse: 0
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 33275
% 38.11/38.52 Kept: 8581
% 38.11/38.52 Inuse: 451
% 38.11/38.52 Deleted: 24
% 38.11/38.52 Deletedinuse: 9
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 50640
% 38.11/38.52 Kept: 11210
% 38.11/38.52 Inuse: 472
% 38.11/38.52 Deleted: 24
% 38.11/38.52 Deletedinuse: 9
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 62359
% 38.11/38.52 Kept: 13539
% 38.11/38.52 Inuse: 511
% 38.11/38.52 Deleted: 24
% 38.11/38.52 Deletedinuse: 9
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 79435
% 38.11/38.52 Kept: 16939
% 38.11/38.52 Inuse: 593
% 38.11/38.52 Deleted: 25
% 38.11/38.52 Deletedinuse: 9
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 88254
% 38.11/38.52 Kept: 18962
% 38.11/38.52 Inuse: 639
% 38.11/38.52 Deleted: 28
% 38.11/38.52 Deletedinuse: 11
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying clauses:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 99175
% 38.11/38.52 Kept: 21083
% 38.11/38.52 Inuse: 674
% 38.11/38.52 Deleted: 416
% 38.11/38.52 Deletedinuse: 12
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 110768
% 38.11/38.52 Kept: 23593
% 38.11/38.52 Inuse: 719
% 38.11/38.52 Deleted: 417
% 38.11/38.52 Deletedinuse: 13
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 123070
% 38.11/38.52 Kept: 25999
% 38.11/38.52 Inuse: 734
% 38.11/38.52 Deleted: 418
% 38.11/38.52 Deletedinuse: 14
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 134929
% 38.11/38.52 Kept: 28413
% 38.11/38.52 Inuse: 768
% 38.11/38.52 Deleted: 419
% 38.11/38.52 Deletedinuse: 14
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 151959
% 38.11/38.52 Kept: 30871
% 38.11/38.52 Inuse: 803
% 38.11/38.52 Deleted: 419
% 38.11/38.52 Deletedinuse: 14
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 168366
% 38.11/38.52 Kept: 33133
% 38.11/38.52 Inuse: 823
% 38.11/38.52 Deleted: 420
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 172626
% 38.11/38.52 Kept: 35407
% 38.11/38.52 Inuse: 828
% 38.11/38.52 Deleted: 420
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 183883
% 38.11/38.52 Kept: 37412
% 38.11/38.52 Inuse: 853
% 38.11/38.52 Deleted: 420
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 192397
% 38.11/38.52 Kept: 39501
% 38.11/38.52 Inuse: 898
% 38.11/38.52 Deleted: 420
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying clauses:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 207635
% 38.11/38.52 Kept: 42445
% 38.11/38.52 Inuse: 947
% 38.11/38.52 Deleted: 740
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 237889
% 38.11/38.52 Kept: 45412
% 38.11/38.52 Inuse: 967
% 38.11/38.52 Deleted: 740
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 266896
% 38.11/38.52 Kept: 47531
% 38.11/38.52 Inuse: 972
% 38.11/38.52 Deleted: 740
% 38.11/38.52 Deletedinuse: 15
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52 Resimplifying inuse:
% 38.11/38.52 Done
% 38.11/38.52
% 38.11/38.52
% 38.11/38.52 Intermediate Status:
% 38.11/38.52 Generated: 290827
% 38.11/38.52 Kept: 50705
% 106.28/106.74 Inuse: 987
% 106.28/106.74 Deleted: 740
% 106.28/106.74 Deletedinuse: 15
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 301213
% 106.28/106.74 Kept: 52826
% 106.28/106.74 Inuse: 1017
% 106.28/106.74 Deleted: 740
% 106.28/106.74 Deletedinuse: 15
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 309606
% 106.28/106.74 Kept: 56729
% 106.28/106.74 Inuse: 1021
% 106.28/106.74 Deleted: 740
% 106.28/106.74 Deletedinuse: 15
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 318493
% 106.28/106.74 Kept: 60723
% 106.28/106.74 Inuse: 1025
% 106.28/106.74 Deleted: 740
% 106.28/106.74 Deletedinuse: 15
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying clauses:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 326353
% 106.28/106.74 Kept: 64204
% 106.28/106.74 Inuse: 1026
% 106.28/106.74 Deleted: 868
% 106.28/106.74 Deletedinuse: 15
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 340863
% 106.28/106.74 Kept: 66349
% 106.28/106.74 Inuse: 1047
% 106.28/106.74 Deleted: 869
% 106.28/106.74 Deletedinuse: 16
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 358783
% 106.28/106.74 Kept: 68710
% 106.28/106.74 Inuse: 1057
% 106.28/106.74 Deleted: 869
% 106.28/106.74 Deletedinuse: 16
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 373490
% 106.28/106.74 Kept: 70928
% 106.28/106.74 Inuse: 1072
% 106.28/106.74 Deleted: 869
% 106.28/106.74 Deletedinuse: 16
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 386047
% 106.28/106.74 Kept: 73050
% 106.28/106.74 Inuse: 1102
% 106.28/106.74 Deleted: 870
% 106.28/106.74 Deletedinuse: 17
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 397230
% 106.28/106.74 Kept: 75050
% 106.28/106.74 Inuse: 1131
% 106.28/106.74 Deleted: 870
% 106.28/106.74 Deletedinuse: 17
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 411303
% 106.28/106.74 Kept: 77613
% 106.28/106.74 Inuse: 1152
% 106.28/106.74 Deleted: 871
% 106.28/106.74 Deletedinuse: 18
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 425010
% 106.28/106.74 Kept: 80500
% 106.28/106.74 Inuse: 1177
% 106.28/106.74 Deleted: 871
% 106.28/106.74 Deletedinuse: 18
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying clauses:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 435305
% 106.28/106.74 Kept: 82560
% 106.28/106.74 Inuse: 1198
% 106.28/106.74 Deleted: 1512
% 106.28/106.74 Deletedinuse: 18
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 448519
% 106.28/106.74 Kept: 86410
% 106.28/106.74 Inuse: 1217
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 474303
% 106.28/106.74 Kept: 89405
% 106.28/106.74 Inuse: 1227
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 507837
% 106.28/106.74 Kept: 92505
% 106.28/106.74 Inuse: 1237
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 542150
% 106.28/106.74 Kept: 95751
% 106.28/106.74 Inuse: 1247
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 562769
% 106.28/106.74 Kept: 98151
% 106.28/106.74 Inuse: 1262
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 589500
% 106.28/106.74 Kept: 102241
% 106.28/106.74 Inuse: 1287
% 106.28/106.74 Deleted: 1513
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying clauses:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 611304
% 106.28/106.74 Kept: 105045
% 106.28/106.74 Inuse: 1307
% 106.28/106.74 Deleted: 1999
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 626823
% 106.28/106.74 Kept: 107085
% 106.28/106.74 Inuse: 1330
% 106.28/106.74 Deleted: 1999
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 642700
% 106.28/106.74 Kept: 109877
% 106.28/106.74 Inuse: 1347
% 106.28/106.74 Deleted: 1999
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 667499
% 106.28/106.74 Kept: 113399
% 106.28/106.74 Inuse: 1361
% 106.28/106.74 Deleted: 1999
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 679888
% 106.28/106.74 Kept: 116384
% 106.28/106.74 Inuse: 1363
% 106.28/106.74 Deleted: 1999
% 106.28/106.74 Deletedinuse: 19
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74 Resimplifying inuse:
% 106.28/106.74 Done
% 106.28/106.74
% 106.28/106.74
% 106.28/106.74 Intermediate Status:
% 106.28/106.74 Generated: 700619
% 106.28/106.74 Kept: 118409
% 195.72/196.22 Inuse: 1391
% 195.72/196.22 Deleted: 1999
% 195.72/196.22 Deletedinuse: 19
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 712505
% 195.72/196.22 Kept: 120510
% 195.72/196.22 Inuse: 1407
% 195.72/196.22 Deleted: 1999
% 195.72/196.22 Deletedinuse: 19
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying clauses:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 725364
% 195.72/196.22 Kept: 122682
% 195.72/196.22 Inuse: 1422
% 195.72/196.22 Deleted: 2168
% 195.72/196.22 Deletedinuse: 19
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 747090
% 195.72/196.22 Kept: 124768
% 195.72/196.22 Inuse: 1437
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 764959
% 195.72/196.22 Kept: 126896
% 195.72/196.22 Inuse: 1462
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 782588
% 195.72/196.22 Kept: 128906
% 195.72/196.22 Inuse: 1489
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 794317
% 195.72/196.22 Kept: 130924
% 195.72/196.22 Inuse: 1502
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 806328
% 195.72/196.22 Kept: 132924
% 195.72/196.22 Inuse: 1511
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 822659
% 195.72/196.22 Kept: 136175
% 195.72/196.22 Inuse: 1523
% 195.72/196.22 Deleted: 2169
% 195.72/196.22 Deletedinuse: 20
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 830006
% 195.72/196.22 Kept: 139113
% 195.72/196.22 Inuse: 1524
% 195.72/196.22 Deleted: 2170
% 195.72/196.22 Deletedinuse: 21
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 848432
% 195.72/196.22 Kept: 141553
% 195.72/196.22 Inuse: 1547
% 195.72/196.22 Deleted: 2170
% 195.72/196.22 Deletedinuse: 21
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 888169
% 195.72/196.22 Kept: 144179
% 195.72/196.22 Inuse: 1552
% 195.72/196.22 Deleted: 2171
% 195.72/196.22 Deletedinuse: 22
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying clauses:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 928074
% 195.72/196.22 Kept: 146709
% 195.72/196.22 Inuse: 1557
% 195.72/196.22 Deleted: 2393
% 195.72/196.22 Deletedinuse: 22
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 952488
% 195.72/196.22 Kept: 150229
% 195.72/196.22 Inuse: 1567
% 195.72/196.22 Deleted: 2393
% 195.72/196.22 Deletedinuse: 22
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 967022
% 195.72/196.22 Kept: 152259
% 195.72/196.22 Inuse: 1585
% 195.72/196.22 Deleted: 2394
% 195.72/196.22 Deletedinuse: 23
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 979007
% 195.72/196.22 Kept: 154307
% 195.72/196.22 Inuse: 1599
% 195.72/196.22 Deleted: 2394
% 195.72/196.22 Deletedinuse: 23
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 987873
% 195.72/196.22 Kept: 156456
% 195.72/196.22 Inuse: 1602
% 195.72/196.22 Deleted: 2394
% 195.72/196.22 Deletedinuse: 23
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1000608
% 195.72/196.22 Kept: 158676
% 195.72/196.22 Inuse: 1617
% 195.72/196.22 Deleted: 2394
% 195.72/196.22 Deletedinuse: 23
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1016207
% 195.72/196.22 Kept: 160680
% 195.72/196.22 Inuse: 1628
% 195.72/196.22 Deleted: 2395
% 195.72/196.22 Deletedinuse: 24
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1034110
% 195.72/196.22 Kept: 162714
% 195.72/196.22 Inuse: 1640
% 195.72/196.22 Deleted: 2396
% 195.72/196.22 Deletedinuse: 25
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying clauses:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1048565
% 195.72/196.22 Kept: 164732
% 195.72/196.22 Inuse: 1658
% 195.72/196.22 Deleted: 2527
% 195.72/196.22 Deletedinuse: 25
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1062214
% 195.72/196.22 Kept: 166799
% 195.72/196.22 Inuse: 1672
% 195.72/196.22 Deleted: 2527
% 195.72/196.22 Deletedinuse: 25
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1080425
% 195.72/196.22 Kept: 168872
% 195.72/196.22 Inuse: 1682
% 195.72/196.22 Deleted: 2527
% 195.72/196.22 Deletedinuse: 25
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1100003
% 195.72/196.22 Kept: 171211
% 195.72/196.22 Inuse: 1702
% 195.72/196.22 Deleted: 2528
% 195.72/196.22 Deletedinuse: 26
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 195.72/196.22
% 195.72/196.22
% 195.72/196.22 Intermediate Status:
% 195.72/196.22 Generated: 1113184
% 195.72/196.22 Kept: 173407
% 195.72/196.22 Inuse: 1722
% 195.72/196.22 Deleted: 2528
% 195.72/196.22 Deletedinuse: 26
% 195.72/196.22
% 195.72/196.22 Resimplifying inuse:
% 195.72/196.22 Done
% 300.10/300.61 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------